Difference between revisions of "Associative"

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Line 14: Line 14:
 
(3 x 4) x 5
 
(3 x 4) x 5
  
= 12 x 5 = 60
+
= 12 x 5 = '''60'''
  
  
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3 x (4 x 5)
 
3 x (4 x 5)
  
= 3 x 20 = 60
+
= 3 x 20 = '''60'''
  
  
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(3 + 4) + 5
 
(3 + 4) + 5
  
= 7 + 5 = 12
+
= 7 + 5 = '''12'''
  
  
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3 + (4 + 5)
 
3 + (4 + 5)
  
= 3 + 9 = 12
+
= 3 + 9 = '''12'''
  
  
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===Division and subtraction are not associative===
 
===Division and subtraction are not associative===
  
The associative property does not apply to division. The order of successive divisions does make a difference to the final result.
+
The associative property does ''not'' apply to division. The order of successive divisions does make a difference to the final result.
  
 
====Example 3====
 
====Example 3====
(60 / 4) / 5 gives produces a different result from 60 / (4 / 5).
+
(60 / 4) / 5 produces a different result from 60 / (4 / 5).
  
  
Line 58: Line 58:
 
(60 / 4) / 5
 
(60 / 4) / 5
  
= 15 / 5 = 3
+
= 15 / 5 = '''3'''
  
  
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60 / (4 / 5)
 
60 / (4 / 5)
  
= 60 / 0.8 = 75
+
= 60 / 0.8 = '''75'''
  
  
  
 
====Example 4====
 
====Example 4====
The associative property does not apply to subtraction.
+
The associative property does not apply to subtraction either.  
  
 
(5 - 4) - 3 gives a different result from 5 - (4 - 3).
 
(5 - 4) - 3 gives a different result from 5 - (4 - 3).
Line 79: Line 79:
 
(5 - 4) - 3
 
(5 - 4) - 3
  
= 1 - 3 = -2
+
= 1 - 3 = '''-2'''
  
  
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5 - (4 - 3)
 
5 - (4 - 3)
  
= 5 - 1 = 4
+
= 5 - 1 = '''4'''
 
+
 
+
  
 
== See also ==
 
== See also ==
 
* [[Commutative]]
 
* [[Commutative]]
 
* [[Distributive]]
 
* [[Distributive]]

Revision as of 15:50, 5 August 2016

Maths.

Multiplication and addition are associative

The associative property of multiplication means that the order in which successive multiplications are done makes no difference to the final result.

Example 1

(3 x 4) x 5 gives the same final result as 3 x (4 x 5).


In the first case:

(3 x 4) x 5

= 12 x 5 = 60


In the second case:

3 x (4 x 5)

= 3 x 20 = 60


Example 2

The associative property also applies to addition.

(3 + 4) + 5 gives the same final result as 3 + (4 + 5).


In the first case:

(3 + 4) + 5

= 7 + 5 = 12


In the second case:

3 + (4 + 5)

= 3 + 9 = 12


Division and subtraction are not associative

The associative property does not apply to division. The order of successive divisions does make a difference to the final result.

Example 3

(60 / 4) / 5 produces a different result from 60 / (4 / 5).


In the first case:

(60 / 4) / 5

= 15 / 5 = 3


In the second case:

60 / (4 / 5)

= 60 / 0.8 = 75


Example 4

The associative property does not apply to subtraction either.

(5 - 4) - 3 gives a different result from 5 - (4 - 3).


In the first case:

(5 - 4) - 3

= 1 - 3 = -2


In the second case:

5 - (4 - 3)

= 5 - 1 = 4

See also